A three generation oscillation analysis of the Super-Kamiokande atmospheric neutrino data beyond one mass scale dominance approximation

In this paper we do a three-generation oscillation analysis of the latest (1144 days) Super-Kamiokande (SK) atmospheric neutrino data going beyond the one mass scale dominance (OMSD) approximation. We fix Δ12=Δ13 (ΔLSND) in the range eV2 as allowed by the results from LSND and other accelerator and reactor experiments on neutrino oscillation and keep Δ23 (ΔATM) and the three mixing angles as free parameters. We incorporate the matter effects, indicate some new allowed regions with small Δ23 (<10−4 eV2) and sin22θ23 close to 0 and discuss the differences with the two-generation and OMSD pictures. In our scenario, the oscillation probabilities for the accelerator and reactor neutrinos involve only two of the mixing angles θ12 and θ13 and one mass scale. But the atmospheric neutrino oscillation is in general governed by both mass scales and all the three mixing angles. The higher mass scale gives rise to Δm2 independent average oscillations for atmospheric neutrinos and does not enter the χ2 analysis as an independent parameter. The Δ23 and the three mixing angles on the other hand appear as independent parameters in the χ2 analysis and the best-fit values of these are determined from an analysis of (a) the SK data, (b) the SK and CHOOZ data. The allowed values of the mixing angles θ12 and θ13 from the above analysis are compared with the constraints from all accelerator and reactor experiments including the latest results from LSND and KARMEN2. Implications for future long baseline experiments are discussed.